Instantaneuos kinematics and manipulability of mobile manipulators

We consider the kinematics of a mobile manipulator that consists of a non-holonomic (or holonomic) mobile platform and a holonomic manipulator mounted atop of the platform. At any fixed time instant and with fixed initial state of the platform these kinematics are viewed as a map from a Hilbert space of controls and manipulator’s joint positions into a taskspace of the mobile manipulator, and called the instantaneous kinematics. The derivative of this map is referred to as the instantaneous analytic Jacobian of the mobile manipulator. By following a procedure defining the pseudoinverse of the Jacobian we derive an instantaneous manipulability matrix and a manipulability measure of the mobile manipulator. The pairs (control, manipulator’s joint position) at which the manipulability matrix becomes singular are called singularities of the mobile manipulator. The manipulability matrix is used in order to introduce an instantaneous manipulability ellipsoid of the mobile manipulator. Theoretical concepts are illustrated with examples of mobile manipulators equipped with both holonomic and non-holonomic mobile platforms. Keywords—mobile manipulator, kinematics, manipulability, non-holonomic system, control system